%%
%% Estensioni matematiche AMS
%%
\usepackage{amsmath}
\usepackage{amssymb} % simboli vari
\usepackage{amsxtra} % varie ed eventuali

%%
%% Font matematici
%%
\usepackage{amsfonts} % \mathcal, \mathbb, \mathfrak
\usepackage{mathrsfs} % \mathscr
\usepackage{eucal}    % \mathcal


%%
%% Tipi di oggetti
%%
\newcommand{\category}[1]{\mathsf{#1}} % categorie
\newcommand{\operad}[1]{\mathscr{#1}}  % operad
\newcommand{\field}[1]{\mathbb{#1}}    % campi numerici
\newcommand{\sheaf}[1]{\mathcal{#1}}   % fasci
\newcommand{\lie}[1]{\mathfrak{#1}}    % algebre di Lie

%%
%% Insiemi notevoli
%%
\newcommand{\setC}{\mathbb{C}}
\newcommand{\setN}{\mathbb{N}}
\newcommand{\setQ}{\mathbb{Q}}
\newcommand{\setZ}{\mathbb{Z}}
\newcommand{\setR}{\mathbb{R}}

%%
%% Campi numerici
%%
\newcommand{\fk}{\Bbbk}\let\k=\fk


%%
%% Algebra lineare
%%
\newcommand{\lspan}[1]{\left\langle#1\right\rangle} % span lineare
\newcommand{\cplx}[1]{#1^{}_\setC} % complessificato

\newcommand{\inner}[3][]{( #2|#3 )_{#1}}   % prodotto scalare
\newcommand{\ip}[3][]{( #2|#3 )_{#1}}   % prodotto scalare
\newcommand{\ipsq}[3][]{[ #2|#3 ]_{#1}}   % prodotto scalare
\newcommand{\ipang}[3][]{\langle #2|#3 \rangle_{#1}}   % prodotto scalare

\newcommand{\pairing}[3][]{\langle #2,#3 \rangle_{#1}} % accoppiamento di dualit{\`a}

\newcommand{\rdl}[1]{{#1}\spcheck}   % duale a dx
\newcommand{\ldl}[1]{{}\spcheck{#1}} % duale a sn


%%
%% Operatori differenziali
%%
\newcommand{\del}{\partial}
\newcommand{\delbar}{\bar\partial}
\newcommand{\ud}{\mathrm{d}}


%%
%% Omologia, coomologia, etc.
%%
\newcommand{\Htop}{H^{\textrm{top}}}


%%
%% Esponenti
%%
\newcommand{\tp}[1]{\sp{\otimes #1}} % tensor power
\newcommand{\xp}[1]{\sp{\land #1}}   % exterior power

\newcommand{\sptext}[1]{\sp{\text{#1}}}
\newcommand{\sbtext}[1]{\sb{\text{#1}}}


%%
%% Gruppi
%%
\newcommand{\Perm}[1]{\mathfrak{S}_{#1}} % gruppo simmetrico
\newcommand{\Stab}{\textrm{Stab}}


%%
%% Simboli vari
%%
\DeclareMathOperator{\Hom}{Hom} % Hom-set
\DeclareMathOperator{\End}{End} % Endomorphisms
\DeclareMathOperator{\Iso}{Iso} % Isomorphisms
\DeclareMathOperator{\Aut}{Aut} % Automorphisms

\DeclareMathOperator{\Dom}{Dom} % Domain of a map
\DeclareMathOperator{\Codom}{Codom} % codomain of map
\DeclareMathOperator{\dom}{dom} % Domain of a map
\DeclareMathOperator{\codom}{codom} % codomain of map

\DeclareMathOperator{\diag}{diag} %diagonal

\DeclareMathOperator{\id}{id}
\DeclareMathOperator{\Id}{Id}

\DeclareMathOperator{\tr}{tr}
\DeclareMathOperator{\Tr}{Tr}

\newcommand{\Diff}{\textrm{Diff}}   % Diffeomorfismi
\newcommand{\Def}{\textrm{Def}}     % Deformazioni
\DeclareMathOperator{\Coeff}{Coeff} % coefficiente di Laurent

\DeclareMathOperator{\ev}{ev}       % evaluation map in a rigid category
\DeclareMathOperator{\coev}{coev}   % coevaluation map

\newcommand{\isoarrow}{\stackrel{\sim}{\to}}       % isomorphism arrow
\newcommand{\opp}{\sptext{opp}}

\DeclareMathOperator{\Src}{Src}
\DeclareMathOperator{\Tgt}{Tgt}
\DeclareMathOperator{\In}{In}
\DeclareMathOperator{\Out}{Out}
\DeclareMathOperator{\Leg}{Leg}

\DeclareMathOperator{\sgn}{sgn}
\DeclareMathOperator{\sign}{sign}


%%
%% Frazioni notevoli
%%
\newcommand{\onehalf}{\frac{1}{2}}
\newcommand{\onethird}{\frac{1}{3}}
\newcommand{\oneof}[1]{\frac{1}{#1}}

\newcommand{\half}[1]{\frac{#1}{2}}
\newcommand{\third}[1]{\frac{#1}{3}}

\newcommand{\twothirds}{\frac{2}{3}}


%%
%% Costanti
%%
\newcommand{\I}{\mathrm{i}}   % unit{\`a} immaginaria
\newcommand{\U}{\sqrt{-1}}    % radice di -1

\newcommand{\E}{\mathrm{e}}   % numero di Nepero

\newcommand{\inv}{\sp{-1}}


%%
%% Costruzioni
%%
\newcommand{\abs}[1]{\lvert#1\rvert}
\newcommand{\norm}[1]{\lVert#1\rVert}
\newcommand{\card}[1]{\lvert#1\rvert}

\newcommand{\correlator}[1]{\langle #1 \rangle} % correlatore di Schwinger
\newcommand{\avg}[2][V]{\langle #2 \rangle_{#1}^{}} % media


%%
%% Simboli vari
%%
\let\geq=\geqslant % come dice Campanato, il segno di '>' sottolineato {\'e}
\let\leq=\leqslant % stato introdotto solo perch{\`e} i tipografi non
                   % disponevano del *vero* segno di maggiore-o-uguale...

\newcommand{\oo}{\infty}


%%
%% Categorie
%%
\newcommand{\catSet}{\category{Set}}            % category of Sets
\newcommand{\catVect}[1][]{\category{Vect}_{#1}}% Vector spaces over a field
\newcommand{\catMod}{\category{Mod}}            % Modules over a ring
\newcommand{\catBraid}{\category{Braid}}        % category of braids
 
\newcommand{\EndOp}[1][]{\operad{E}_{#1}} % Endomorphism Operad


%%% Local Variables: 
%%% mode: latex
%%% TeX-master: "index.tex"
%%% x-symbol-8bits: nil
%%% End: 
